Backward consistency and sense of direction in advanced distributed systems

Abstract

The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the point-to-point model and is realistic for systems where a communication link can connect only two entities. However, in systems which use more advanced communication and interconnection technology such as buses, optical networks, wireless communication media, etc., and more importantly, heterogeneous systems (such as internet) which include any combination of the above, local orientation can not be assumed. In this paper we consider a new type of consistency which we shall call backward consistency and which, unlike sense of direction, can exist even without local orientation. Thus, unlike all previous forms of consistency, it can be found (or designed) in advanced distributed systems. We study backward consistency both in terms of its relationship with the traditional properties of local orientation and (weak) sense of direction, and with respect to symmetries of the edge labelings and of the naming functions. We prove that backward consistency is computationally equivalent to sense of direction; in other words, it is possible to take advantage of the computational power of sense of direction even in absence of local orientation.